Jeremy Rouse

Affiliation: University of Illinois, Urbana

Email: jarouse@math.uiuc.edu

Title Of Talk: Bounds for the coefficients of powers of the $\Delta$-function

Abstract: Let \[ \sum_{n=k}^{\infty} \tau_{k}(n) q^{n} = q^{k} \prod_{n=1}^{\infty} (1-q^{n})^{24k}. \] Work of Deligne implies that there is a constant $C_{k}$ so that $|\tau_{k}(n)| \leq C_{k} d(n) n^{(12k-1)/2}$. We will show that $C_{k}$ tends to zero very rapidly as $k \to \infty$.


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